Diagnosis
You've found the Tailgater's messiest design flaw. The grease management system—the channel in the drip tray and the little hole that drains into a cup—clogs easily, leading to overflow inside the grill and a real cleanup headache.
How to Fix It
You need to be proactive. 1) After every 2-3 cooks, or after any particularly greasy cook, let the grill cool. 2) Pull out the drip tray. 3) Use a putty knife or grill scraper to push the congealed grease and gunk from the channel toward the drain hole. 4) Detach the grease cup (a standard aluminum tin) and empty it. 5) I line my cup with heavy-duty foil for easy cleanup—just crumple and replace. 6) Before reassembling, ensure the drain hole in the tray is completely clear by poking a stick or grill tool through it.
If That Didn't Work
If grease is still leaking from places other than the cup, the drip tray might be warped or not seated perfectly. Make absolutely sure it's pushed all the way back and is sitting flat. Also, avoid pouring liquids or overly watery marinades directly on meat, as they thin the grease and make it run everywhere.
Heads Up
Never let the grease cup overflow. A full cup can drip onto the hot firepot or the auger motor assembly underneath, causing a flare-up or, worse, a grease fire inside the base of the grill. Check it religiously during long cooks.